Free Boundary Problems in PDEs and Particle Systems

• Main Authors: Carinci, Gioia (Author), De Masi, Anna (Author), Giardinà, Cristian (Author), Presutti, Errico (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: SpringerBriefs in Mathematical Physics, 12
• Subjects: Mathematics.; Partial differential equations.; Probabilities.; Mathematical physics.; Physics.; Statistical physics.; Dynamical systems.; Thermodynamics.; Heat engineering.; Heat transfer.; Mass transfer.; Partial Differential Equations.; Statistical Physics, Dynamical Systems and Complexity.; Mathematical Physics.; Probability Theory and Stochastic Processes.; Mathematical Methods in Physics.; Engineering Thermodynamics, Heat and Mass Transfer.

In this volume a theory for models of transport in the presence of a free boundary is developed. Macroscopic laws of transport are described by PDE's. When the system is open, there are several mechanisms to couple the system with the external forces. Here a class of systems where the interacti...

Table of Contents:

• Introduction
• Part I The basic model
• Introduction to Part I
• The basic model, definitions and results
• Regularity properties of the barriers
• Lipschitz and L1 estimates
• Mass transport inequalities
• The limit theorems on barriers
• Brownian motion and the heat equation
• Existence of optimal sequences
• Proof of the main theorem
• The basic particle model and its hydrodynamic limit
• Part II Variants of the basic model
• Introduction to Part II
• Independent walkers with current reservoirs
• Beyond diffusive scaling
• Other models.